Least Common Multiple of 3 and 5

Least common multiple or lowest common denominator (LCD) can be calculated in three ways;

• Least Common Multiple of 3 and 5 by Prime method
• Least Common Multiple of 3 and 5 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 3 and 5. First we will calculate the prime factors of 3 and 5.

Prime Factorization of 3

Prime factors of 3 are 3. Prime factorization of 3 in exponential form is:

3 = 3¹

Prime Factorization of 5

Prime factors of 5 are 5. Prime factorization of 5 in exponential form is:

5 = 5¹

Now multiplying the highest exponent prime factors to calculate the LCM of 3 and 5.

LCM(3,5) = 3¹×5¹
LCM(3,5) = 15

Factors of 3

List of positive integer factors of 3 that divides 3 without a remainder.

1, 3

Factors of 5

List of positive integer factors of 5 that divides 5 without a remainder.

1, 5

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 3 and 5, than apply into the LCM equation.

GCF(3,5) = 1
LCM(3,5) = ( 3 × 5) / 1
LCM(3,5) = 15 / 1
LCM(3,5) = 15

(i) The LCM of 5 and 3 is associative

LCM of 3 and 5 = LCM of 5 and 3

1. What is the LCM of 3 and 5?

Answer: LCM of 3 and 5 is 15.

2. What are the Factors of 3?

Answer: Factors of 3 are 1, 3. There are 2 integers that are factors of 3. The greatest factor of 3 is 3.

3. What are the Factors of 5?

Answer: Factors of 5 are 1, 5. There are 2 integers that are factors of 5. The greatest factor of 5 is 5.

4. How to Find the LCM of 3 and 5?

Answer:

Least Common Multiple of 3 and 5 = 15

Step 1: Find the prime factorization of 3

3 = 3

Step 2: Find the prime factorization of 5

5 = 5

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 15 = 3 x 5

Step 4: Therefore, the least common multiple of 3 and 5 is 15.